The graph of a cosine function shows a reflection over the x-axis, an amplitude of 2, a period of 4, and a phase shift of 0.5 to the right.
Which is the equation of the function described?
y = Acos (Bx + C)
A = the amplitude = 2
Since this is reflected over the x axis, we have A = -2
B = 2pi / period = 2pi / 4 = pi/2
To find C ....the point (.5, -2) is on the graph ....so.....
-2 = -2cos (pi * .5 / 2 + C) divide through by -2
1 = cos ( pi *.5 / 2 + C)
1 = cos ( pi/4 + C)
arccos(1) = pi/4 + C
0 = pi/4 + C
C = - pi/4
The function is
f(x) = -2cos ( pi * x / 2 - pi/4 )
Here's a graph : https://www.desmos.com/calculator/eqbmyly3sk